I think people are reading far too much into this and have complicated the situation. Why call the first insurer? You only call the insurer if you or anyone on your policy has had an accident. But you didn't have an accident, it was your girlfriend that had the accident, and as your girlfriend had nothing to do with your 1st insurer. It pretty simple logic TBH.
BUT... by contacting the first insurer, haven't you opened a bag of worms for yourself? Dan555 says it can never come back to haunt you. Well perhaps it could. (I can't believe nobody has picked this up already)
You have two cars insured in your name. The 2nd car however also has your gf as a named driver. It's pretty obvious is it not that your girlfriend is the the main driver of the 2nd vehicle? On that 2nd insurance policy you should be down as the named driver, not her.
If I've read this correctly, I hope the two insurance companies don't talk to each other. The only reason I can think of for someone to insure a car as a named driver rather than the main driver is to reduce their insurance premium. Is that the reason you had her on as a named driver? Hopefully your 2nd insurer won't pick that up. 